Unreflectable greenscreen-plate
In my opinion it makes no sense to generate CG elements to be color keyed out when you can generate the perfect matte directly as an Alpha Channel. 

In real life chroma key is used because there is no way to generate transparency and occlusion information directly using a camera. No need to replicate such laborious and imprecise workflow when generating CGI.

You can use to use a Holdout shader.


  The Holdout shader node is used to create a “hole” in the image with zero alpha transparency, which is useful for compositing 


Enable Film>Transparent and Save the image in a format that supports an alpha channel (like OpenEXR) and composite in other software with no further processing other than distorting the image to match the perspective of the screen. If you save in a format that does not support alpha then you can save the black and white alpha information as a separate file and use that to key the image.



If you absolutely must use green, because you love doing things the hard way, or with extra work, then you can use a shader that is only visible to the camera but transparent for the rest of the scene. It will not create any reflection or unwanted green spill in any of the surrounding surfaces. Using a Light Path node and using the Is Camera Ray to control the mix of shaders will allow you to do what you want.



The downside of both of these approaches is that the image on the screen will not affect the rest of the scene in any way, making the integration less realistic. A monitor is an emissive surface that would both illuminate and be reflected on other objects. The most realistic way to do this would be to integrate the image as part of the material used on the screen directly.